Train relative positioning method based on digital track map

Abstract

The invention relates to a train positioning method based on a digital track map, which belongs to the technical field of satellite navigation and track traffic positioning, and is characterized in that a track is fitted by acquired track data to obtain a high-precision track curve model. Then, in the train positioning process, the train position calculated by the GNSS is matched with the fitted track curve, and a track constraint optimization method is adopted to correct the train position. A GNSS positioning result is projected to a nearest point of a fitting track curve, deviation correction is carried out in combination with track geometric information, positioning errors caused by environmental interference are eliminated, and therefore the relative positioning precision of a train is improved; according to the method, the train positioning precision is further improved by performing accurate fitting on the track line features and combining a global navigation satellite system (GNSS) positioning technology, the ambiguity fixing rate is effectively improved, and the problems of insufficient train positioning precision, low ambiguity fixing rate and the like in the prior art are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite navigation and rail transit positioning, and particularly relates to a train positioning method based on a digital track map, and more particularly to a train positioning technology based on a digital track map and an orbit fitting method. Background Art

[0002] With the popularization of the Global Navigation Satellite System (GNSS), train positioning technology has become a key technology in railway traffic management and safety monitoring. The accuracy of GNSS positioning technology is crucial for train tracks, vehicle speeds, and operational safety. However, due to factors such as hardware errors of on-vehicle track equipment, multipath effects of GNSS signals, and occlusion, traditional GNSS positioning is prone to positioning errors in certain environments, especially in complex environments such as high-density urban tracks or tunnels.

[0003] In order to improve positioning accuracy, recent research has tended to combine digital track maps (DTMs) with GNSS data and use track alignment features for map matching. Although such technologies have been proposed and applied, existing orbit fitting methods still face certain challenges when dealing with complex changes in track alignment, especially in terms of how to efficiently improve positioning accuracy and ambiguity fixing rate.

[0004] There are at least the following problems in the prior art: accuracy loss and curve feature loss. In the prior art, many studies have used multiple broken lines to approximately describe the curve segments of the track. Although this method can achieve a preliminary description of the track alignment, it cannot fully reflect the overall characteristics of the track and often leads to accuracy loss of trajectory data. Because the approximation method of multiple broken lines actually uses relatively rough line segments to replace complex curves, this is insufficient in the railway field where high-precision positioning requirements are relatively high. Especially when the track alignment has complex bends, the simplified processing of the broken lines fails to completely retain the detailed information of the curve, thereby affecting the positioning accuracy and geometric description of the track.

[0005] Insufficient simplification of track alignment and complexity of curve recognition. Existing track alignment simplification methods, such as heuristic algorithms and curve fitting based on cubic B-splines, although they can perform preliminary simplification and fitting of trajectory data, the accuracy of these methods is limited. Especially when dealing with complex railway tracks, they cannot well adapt to the changes of different trajectories. In addition, some methods such as heuristic algorithms require the selection of initial points, and the algorithms are complex, resulting in high computational costs and being easily affected by initial conditions.

[0006] The fitting accuracy is affected by outlier (anomaly) data. Many existing methods, such as the Kalman filtering algorithm or the least squares (LS) method, fail to effectively process outliers (anomalies) in trajectory data, and these outliers may significantly reduce the accuracy of track alignment fitting. Especially in complex track environments, the presence of outliers often leads to unreliable fitting results. Summary of the Invention

[0007] In view of the above problems, the present invention provides a train relative positioning method based on a digital track map. The trajectory data collected by the present invention is used to fit the track to obtain a high-precision track curve model. Then, during the train positioning process, the position of the train calculated by GNSS is matched with the fitted track curve, and an orbit constraint optimization method is used to correct the position of the train. By projecting the GNSS positioning result to the nearest point of the fitted track curve and combining the track geometric information for deviation correction, the positioning error caused by environmental interference is eliminated, thereby improving the relative positioning accuracy of the train; the present invention accurately fits the track line characteristics, combines the global satellite navigation system GNSS positioning technology, further improves the train positioning accuracy, and effectively improves the ambiguity fixation rate, solving the problems of insufficient train positioning accuracy and low ambiguity fixation rate in the prior art.

[0008] The present invention provides a train relative positioning method based on a digital track map, including:

[0009] Step S1: Let i = 1. When i = 1, it represents the first epoch trajectory point;

[0010] Step S2: Based on the position information of the i-th epoch trajectory point, obtain the azimuth angle and the corresponding approximate curvature of the i-th epoch trajectory point;

[0011] Step S3: Smoothly filter the azimuth angle and the corresponding approximate curvature of the i-th epoch trajectory point to obtain the filtered approximate curvature of the i-th epoch trajectory point;

[0012] Step S4: Obtain the two-dimensional plane alignment of the i-th epoch trajectory point based on the filtered approximate curvature of the i-th epoch trajectory point;

[0013] Step S5: Traverse I epoch trajectory points to obtain the two-dimensional plane alignments of each epoch trajectory point;

[0014] Step S6: Fit the two-dimensional plane alignments of multiple epoch trajectory points to obtain a fitting curve polynomial, which is characterized as a digital track map;

[0015] Step S7: Perform train positioning based on the digital track map.

[0016] Optionally, the specific steps of step S4 include:

[0017] Step S41: Determine whether the approximate curvature of the filtered i-th epoch trajectory point is less than the curvature threshold. If so, the i-th epoch trajectory point is located on line segment A i , adjust the starting point and ending point of line segment A i to obtain the corresponding updated line segment A' i , and enter Step S42; if not, the i-th epoch trajectory point is located on curve segment C i , and enter Step S43;

[0018] Step S42: Determine whether the updated line segment A' i meets the preset lateral error. If it meets, the i-th epoch trajectory point is located on the transition curve segment B i , adjust the starting point and ending point of the transition curve segment B i to obtain the corresponding updated transition curve segment B′ i , and use the corresponding updated transition curve segment B′ i as the two-dimensional plane alignment of the i-th epoch trajectory point; if it does not meet, let i = i + 1, use the updated line segment A' i as the two-dimensional plane alignment of the i-th epoch trajectory point, and return to Step S2;

[0019] Step S43: Adjust the starting point and ending point of curve segment C i to obtain the corresponding updated curve segment C′ i , determine whether the updated curve segment C′ i meets the preset lateral error. If it meets, the i-th epoch trajectory point is located on curve segment C i , and use the corresponding updated curve segment C′ i as the two-dimensional plane alignment of the i-th epoch trajectory point; if it does not meet, let i = i + 1, use the updated line segment A' i as the two-dimensional plane alignment of the i-th epoch trajectory point, and return to Step S2.

[0020] Optionally, the specific steps of Step S7 include:

[0021] Establish an orbit equation based on the digital track map;

[0022] Obtain the state estimation value of the (i - 1)-th epoch trajectory point based on the orbit equation; when i = 1, the (i - 1)-th epoch trajectory point is located at the starting point;

[0023] Obtain the state prediction value of the i-th epoch trajectory point based on the state estimation value of the (i - 1)-th epoch trajectory point;

[0024] Obtain the covariance matrix of the i-th epoch trajectory point based on the state prediction value of the i-th epoch trajectory point;

[0025] Obtain the filtering gain matrix of the $i$-th epoch trajectory point based on the covariance matrix of the $i$-th epoch trajectory point;

[0026] Update the state prediction value of the $i$-th epoch trajectory point based on the filtering gain matrix of the $i$-th epoch trajectory point to obtain the state estimation value of the $i$-th epoch trajectory point;

[0027] Traverse the trajectory points of each epoch, obtain the state estimation values of the trajectory points of each epoch, and position the train based on the state estimation values of the trajectory points of each epoch to obtain the final train track.

[0028] Optionally, the expression of the filtering gain matrix of the $i$-th epoch trajectory point is:

[0029]

[0030] where $K$ i is the filtering gain matrix of the $i$-th epoch trajectory point, $H$ i is the observation matrix of the $i$-th epoch trajectory point, $R$ i is the measurement noise covariance matrix of the $i$-th epoch trajectory point, and $P$ i / i-1 is the covariance matrix of the $i$-th epoch trajectory point.

[0031] Optionally, the specific steps of step S6 include:

[0032] Step S61: Based on multiple epoch trajectory points, establish a polynomial curve;

[0033] Step S62: Obtain the fitting residual of the $i$-th epoch trajectory point to the polynomial curve and the sum of the squares of the fitting residuals;

[0034] Step S63: Minimize the sum of the squares of the polynomial curve fitting residuals to obtain the curve fitting objective function,

[0035] Step S64: Solve the minimum point of the curve fitting objective function;

[0036] Step S65: Take the minimum point of the curve fitting objective function as the optimal parameter to be determined;

[0037] Step S66: Substitute the optimal parameter to be determined into the polynomial curve matrix to obtain the polynomial of the fitting curve.

[0038] Optionally, the expression of the curve fitting objective function is:

[0039]

[0040] where is the sum of the squares of the residuals, and $\delta$ iis the fitting residual of the i-th epoch trajectory point, δ represents the residual, B is the curve fitting objective function, and x i represents the x-axis coordinate status value of the i-th epoch trajectory point, C(.) represents the polynomial function, and y i is the y-axis coordinate status value of the i-th epoch trajectory point, where i = 1, 2, 3 … I, and I represents the total number of epochs.

[0041] Optionally, the position information of the i-th epoch trajectory point is obtained through the Global Navigation Satellite System (GNSS).

[0042] Optionally, the curvature threshold is used to divide the straight line shape and the curve shape.

[0043] Optionally, the preset lateral error is used to divide the circular curve and the transition curve.

[0044] Optionally, the fitting curve polynomial includes a straight line shape, a circular curve shape, and a transition curve shape.

[0045] Compared with the prior art, the present invention has at least the following beneficial effects:

[0046] (1) The present invention introduces the orbit fitting technology to accurately constrain the train position based on the GNSS positioning data;

[0047] (2) The present invention optimizes the least squares fitting algorithm through an adaptive weight factor to accurately describe the orbit line shape characteristics, and combines the GNSS positioning data for accurate matching, thereby greatly improving the positioning accuracy. Especially in a complex orbit environment, the ambiguity fixation rate can be significantly improved;

[0048] (3) The present invention utilizes the geometric characteristics in the orbit fitting result to assist the GNSS solution and improve the ambiguity fixation rate. Especially in a complex environment, the reliability of the positioning system is significantly enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The drawings are only for the purpose of showing specific embodiments and are not considered as a limitation to the present invention.

[0050] Figure 1 is a schematic diagram of the train relative positioning method based on the digital track map in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0051] To more clearly understand the above objects, features, and advantages of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other. Additionally, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0052] A specific embodiment of the present invention, such as Figure 1 , discloses a train relative positioning method based on a digital track map, and the specific implementation steps include:

[0053] Step S1: Collect multiple epoch track points at the center along the railway line;

[0054] It can be understood that the "epoch" refers to the sampling moment;

[0055] According to the curvature characteristics of the plane alignment, set a curvature threshold; let i = 1. When i = 1, it represents the first epoch track point;

[0056] Step S2: Obtain the position information of the i-th epoch track point through the Global Navigation Satellite System (GNSS);

[0057] Based on the circular arc tangent method and the position information of the i-th epoch track point, obtain the azimuth angle of the i-th epoch track point;

[0058] It can be understood that the azimuth angle of each track point at the center of the railway line refers to the angle between the forward direction along the center line of the railway line and the true north direction with the observation point as the starting point;

[0059] Optionally, the expression for the azimuth angle of the i-th epoch track point is:

[0060]

[0061] where θ i is the azimuth angle of the i-th epoch track point, and θ i ∈[0°, 360°]; x' i is the x-axis state value of the (i + 1)-th epoch track point in the circular arc tangent direction, y' i is the y-axis coordinate of the (i + 1)-th epoch track point in the circular arc tangent direction, x' p,i+1 is the x-axis projection coordinate of the (i + 1)-th epoch track point in the circular arc tangent direction, and y' p,i+1 is the y-axis projection coordinate of the (i + 1)-th epoch track point in the circular arc tangent direction.

[0062] Obtain the approximate curvature of the i-th epoch track point, and the expression is:

[0063]

[0064] Among them, ρ i is the approximate curvature of the (i + 1)-th epoch trajectory point; dis(i, i + 1) is the projected distance between the coordinates of the (i + 1)-th epoch trajectory point and the i-th epoch trajectory point.

[0065] Step S3: Considering the measurement error, use the moving average method to smooth-filter the azimuth angle and the corresponding approximate curvature of the i-th epoch trajectory point to obtain the filtered approximate curvature of the i-th epoch trajectory point;

[0066] Step S4: Obtain the two-dimensional planar alignment of the i-th epoch trajectory point based on the filtered approximate curvature of the i-th epoch trajectory point;

[0067] The specific steps of Step S4 include:

[0068] Step S41: Determine whether the filtered approximate curvature of the i-th epoch trajectory point is less than the curvature threshold. If so, the i-th epoch trajectory point is located on the straight line segment A i . Adjust the starting point and the ending point of the straight line segment A i to obtain the corresponding updated straight line segment A' i , and enter Step S42; if not, the i-th epoch trajectory point is located on the curve segment C i , and enter Step S43;

[0069] Step S42: Determine whether the updated straight line segment A' i meets the preset lateral error. If it meets, the i-th epoch trajectory point is located on the transition curve segment B i . Adjust the starting point and the ending point of the transition curve segment B i to obtain the corresponding updated transition curve segment B′ i , and use the corresponding updated transition curve segment B′ i as the two-dimensional planar alignment of the i-th epoch trajectory point; if it does not meet, let i = i + 1, use the updated straight line segment A' i as the two-dimensional planar alignment of the i-th epoch trajectory point, and return to Step S2;

[0070] Step S43: Adjust the starting point and the ending point of the curve segment C i to obtain the corresponding updated curve segment C′ i . Determine whether the updated curve segment C′ i meets the preset lateral error. If it meets, the i-th epoch trajectory point is located on the curve segment C i . Use the corresponding updated curve segment C′ i as the two-dimensional planar alignment of the i-th epoch trajectory point. If it does not meet, let i = i + 1, and use the updated straight line segment A' iReturn to step S2 for the two-dimensional planar alignment of the i-th epoch trajectory point;

[0071] Optionally, the preset lateral error is used to divide the circular curve and the transition curve;

[0072] Exemplarily, the preset lateral error is 0.25 m;

[0073] Exemplarily, the curvature threshold

[0074] The curvature threshold is used to divide the straight alignment and the curve alignment. If it is less than the threshold, it is a straight alignment; if it is greater than the threshold, it is a curve alignment;

[0075] Step S5: Traverse the I epoch trajectory points to obtain the two-dimensional planar alignments of each epoch trajectory point;

[0076] Step S6: Fit the two-dimensional planar alignments of multiple epoch trajectory points to obtain a fitting curve polynomial, which is characterized as a digital track map; establish a track equation based on the fitting curve polynomial;

[0077] Step S7: Perform train positioning based on the digital track map and the track equation.

[0078] Optionally, the specific steps of step S7 for train positioning based on the digital track map include:

[0079] Establish a track equation based on the digital track map;

[0080] Obtain the state estimate value of the (i - 1)-th epoch trajectory point based on the track equation;

[0081] Obtain the state prediction value of the i-th epoch trajectory point based on the state estimate value of the (i - 1)-th epoch trajectory point;

[0082] Obtain the covariance matrix of the i-th epoch trajectory point based on the state prediction value of the i-th epoch trajectory point;

[0083] Obtain the filter gain matrix of the i-th epoch trajectory point based on the covariance matrix of the i-th epoch trajectory point;

[0084] Update the state prediction value of the i-th epoch trajectory point based on the filter gain matrix of the i-th epoch trajectory point to obtain the state estimate value of the i-th epoch trajectory point;

[0085] Traverse the trajectory points of each epoch to obtain the state estimate values of each epoch trajectory point, and perform train positioning based on the state estimate values of each epoch trajectory point to obtain the final train track;

[0086] Optionally, the expression of the state estimate value of the i-th epoch trajectory point is:

[0087]

[0088] Among them, is the state prediction value of the i-th epoch trajectory point, and Φ i / i-1 is the state transition matrix of the i-th epoch trajectory point, is the state estimation value of the (i - 1)-th epoch trajectory point; The expression for the covariance matrix of the i-th epoch trajectory point is:

[0089]

[0090] Among them, P i-1 is the covariance matrix of the (i - 1)-th epoch trajectory point, Γ i-1 is the process noise driving matrix of the (i - 1)-th epoch trajectory point, Q i-1 is the covariance matrix of the process noise of the (i - 1)-th epoch trajectory point, P i / i-1 is the covariance matrix of the i-th epoch trajectory point;

[0091] The expression for the filtering gain matrix of the i-th epoch trajectory point is:

[0092]

[0093] Among them, K i is the filtering gain matrix of the i-th epoch trajectory point, H i is the observation matrix of the i-th epoch trajectory point, R i is the measurement noise covariance matrix of the i-th epoch trajectory point, P i / i-1 is the covariance matrix of the i-th epoch trajectory point.

[0094] Optionally, the expression of the orbit equation is:

[0095] Dx = F

[0096] Among them, D represents the constraint coefficient matrix of the digital orbit map, F is the constraint constant matrix, and x is the trajectory point state value.

[0097] Optionally, the specific steps to obtain the fitting curve polynomial include:

[0098] Step S61, based on multiple epoch trajectory points, establish a polynomial curve, and the expression is:

[0099]

[0100] Among them, a n is the n-th undetermined coefficient, j = 1, 2, 3... n, C(.) represents the polynomial function; x I represents the derivative value of the trajectory point for the I-th derivative.

[0101] Step S62: Obtain the fitting residual of the \(i\)-th epoch trajectory point to the polynomial curve and the sum of squares of the fitting residuals.

[0102] Step S63: Minimize the sum of squares of the polynomial curve fitting residuals to obtain the curve fitting objective function, with the expression:

[0103]

[0104] where, is the sum of squares of residuals, \(\delta\) i is the fitting residual of the \(i\)-th epoch trajectory point, \(B\) is the curve fitting objective function, \(x\) i represents the \(x\)-axis coordinate status value of the \(i\)-th epoch trajectory point, \(y\) i is the \(y\)-axis coordinate status value of the \(i\)-th epoch trajectory point, \(i = 1, 2, 3 \cdots I\), and \(I\) represents the total number of epochs.

[0105] Step S64: Solve for the minimum point of the curve fitting objective function The expression is:

[0106]

[0107] where, \(a\) k is the \(k\)-th coefficient, \(a\) j is the \(j\)-th coefficient, is the derivative value of the \(x\)-axis coordinate status value of the \(i\)-th epoch trajectory point after \(j + k\) differentiations, \(j\) is the exponent of the trajectory point status value, \(k\) is the exponent of the trajectory point status value to be differentiated, \(j, k \in n\), \(x\) i k is the derivative value of the \(x\)-axis coordinate status value of the \(i\)-th epoch trajectory point after \(k\) differentiations; \(y\) i is the \(y\)-axis coordinate status value of the \(i\)-th epoch trajectory point.

[0108] Step S65: Take the minimum point of the curve fitting objective function as the optimal parameter to be determined;

[0109] Step S66: Substitute the optimal parameter to be determined into the polynomial curve matrix to obtain the polynomial of the fitting curve;

[0110] The expression of the parameter to be determined is:

[0111] A T = X -1 Y

[0112] where, \(A\) represents the parameter to be determined, \(X\) is the trajectory point polynomial matrix, and \(Y\) is the trajectory point observed coordinate column vector.

[0113]

[0114] Optionally, the fitting curve polynomial includes a straight line shape, a circular curve shape, and a transition curve shape;

[0115] Specifically, the expression of the straight line shape is: y = ax + b,

[0116] where,

[0117]

[0118] where, a represents the first coefficient, b represents the second coefficient, and x i is the x-axis coordinate status value of the i-th epoch trajectory point, and y i is the y-axis coordinate status value of the i-th epoch trajectory point, is the mean value of the x-axis coordinate status values, is the mean value of the y-axis coordinate status values.

[0119] The expression of the circular curve is:

[0120] R 2 = (x - x0) 2 + (y - y0) 2 ,

[0121] where, (x0, y0) is the center of the circle, and R 2 is the radius. Among them,

[0122]

[0123] The expression of the transition curve is:

[0124] y = ax 3 + bx 2 + cx + d a = 0, b = 0

[0125] where, y is the y-axis status value of the trajectory point, x is the x-axis status value of the trajectory point, c is the third coefficient, and d is the fourth coefficient.

[0126] As described above, only the preferred specific embodiments of the present invention are provided, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A train relative positioning method based on a digital track map, characterized in that Including: Step S1: Let i = 1. When i = 1, it represents the first epoch trajectory point. Step S2: Based on the position information of the i-th epoch trajectory point, obtain the azimuth angle and the corresponding approximate curvature of the i-th epoch trajectory point. Step S3: Perform smoothing filtering on the azimuth angle and the corresponding approximate curvature of the i-th epoch trajectory point to obtain the filtered approximate curvature of the i-th epoch trajectory point. Step S4: Obtain the two-dimensional planar alignment of the i-th epoch trajectory point based on the filtered approximate curvature of the i-th epoch trajectory point. Step S5: Traverse I epoch trajectory points to obtain the two-dimensional planar alignments of each epoch trajectory point. Step S6: Fit the two-dimensional planar alignments of multiple epoch trajectory points to obtain a fitting curve polynomial, which is characterized as a digital track map. Step S7: Perform train positioning based on the digital track map.

2. The train relative positioning method of the digital track map according to claim 1, characterized in that The specific steps of Step S4 include: Step S41: Determine whether the approximate curvature of the filtered i-th epoch trajectory point is less than the curvature threshold. If so, the i-th epoch trajectory point lies on line segment A i and adjust the starting point and ending point of line segment A i to obtain the corresponding updated line segment A' i , and proceed to Step S42; if not, the i-th epoch trajectory point lies on curve segment C i , and proceed to Step S43; Step S42: Determine whether the updated straight line segment A' i satisfies the preset horizontal error. If it does, the i-th epoch trajectory point is located on the transition curve segment B i , adjust the starting point and ending point of the transition curve segment B i to obtain the corresponding updated transition curve segment B' i , and use the corresponding updated transition curve segment B' i as the two-dimensional plane alignment of the i-th epoch trajectory point; if not, let i = i + 1, and use the updated straight line segment A' i as the two-dimensional plane alignment of the i-th epoch trajectory point, and return to step S2; Step S43: Adjust the starting point and the ending point of curve segment C i to obtain the corresponding updated curve segment C′ i , and determine whether the updated curve segment C′ i satisfies the preset lateral error. If it satisfies, the i-th epoch trajectory point is located on the curve segment C i , and use the corresponding updated curve segment C′ i as the two-dimensional plane linear shape of the i-th epoch trajectory point. If it does not satisfy, let i = i + 1, and use the updated straight line segment A' i as the two-dimensional plane linear shape of the i-th epoch trajectory point, and return to step S2.

3. The method for relative positioning of trains on a digital track map according to claim 1, characterized in that, The specific steps of Step S7 include: Establish an orbit equation based on the digital track map. Obtain the state estimation value of the (i - 1)-th epoch trajectory point based on the orbit equation; when i = 1, the (i - 1)-th epoch trajectory point is at the starting point. Obtain the state prediction value of the i-th epoch trajectory point based on the state estimation value of the (i - 1)-th epoch trajectory point. Obtain the covariance matrix of the i-th epoch trajectory point based on the state prediction value of the i-th epoch trajectory point. Obtain the filtering gain matrix of the i-th epoch trajectory point based on the covariance matrix of the i-th epoch trajectory point. Update the state prediction value of the i-th epoch trajectory point based on the filtering gain matrix of the i-th epoch trajectory point to obtain the state estimation value of the i-th epoch trajectory point. Traverse the trajectory points of each epoch to obtain the state estimation values of each epoch trajectory point, perform train positioning based on the state estimation values of each epoch trajectory point, and obtain the final train orbit.

4. The train relative positioning method using the digital track map according to claim 3, wherein The expression of the filtering gain matrix of the i-th epoch trajectory point is: Among them, K i is the filtering gain matrix of the i-th epoch trajectory point, H i is the observation matrix of the i-th epoch trajectory point, P i is the measurement noise covariance matrix of the i-th epoch trajectory point, P i / i-1 The covariance matrix of the epoch trajectory point of the i-th epoch trajectory point.

5. The train relative positioning method using the digital track map according to claim 1, wherein The specific steps of Step S6 include: Step S61: Based on multiple epoch trajectory points, establish a polynomial curve. Step S62: Obtain the fitting residual of the i-th epoch trajectory point to the polynomial curve and the sum of squares of the fitting residuals. Step S63: Let the sum of squares of the polynomial curve fitting residuals be minimized to obtain a curve fitting objective function. Step S64: Solve the minimum value point of the curve fitting objective function. Step S65: Take the minimum value point of the curve fitting objective function as the optimal parameter to be determined. Step S66: Substitute the optimal parameter to be determined into the polynomial curve matrix to obtain the polynomial of the fitting curve.

6. The train relative positioning method using the digital track map according to claim 5, wherein The expression of the curve fitting objective function is: Among them, is the sum of squared residuals, and δ i is the fitting residual of the i-th epoch trajectory point. δ represents the residual, B is the curve fitting objective function, and x i represents the x-axis coordinate status value of the i-th epoch trajectory point. C(.) represents a polynomial function, and y i is the y-axis coordinate status value of the i-th epoch trajectory point, where i = 1, 2, 3... I, and I represents the total number of epochs.

7. The train relative positioning method using the digital track map according to claim 1, wherein Obtain the position information of the i-th epoch trajectory point through the Global Navigation Satellite System (GNSS).

8. The train relative positioning method using the digital track map according to claim 1, wherein The curvature threshold is used to divide the straight line alignment and the curve alignment.

9. The train relative positioning method of the digital track map according to claim 1, characterized in that The preset lateral error is used to divide the circular curve and the transition curve.

10. The train relative positioning method of the digital track map according to claim 1, characterized in that The fitting curve polynomial includes a straight line shape, a circular curve shape, and a transition curve shape.

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